John,
It's not entirely clear what you mean by 'count' column C, do you mean any
value?
Here's a couple of ideas
Number in A&B anything in C
=SUMPRODUCT((A1:A10=123)*(B1:B10=234)*(C1:C10<>""))
Text in A&B anything in C
=SUMPRODUCT((A1:A10="ABC")*(B1:B10="DEF")*(C1:C10<>""))
Sum column C
=SUMPRODUCT((A1:A10="ABC")*(B1:B10="DEF")*(C1:C10))
--
Mike
When competing hypotheses are otherwise equal, adopt the hypothesis that
introduces the fewest assumptions while still sufficiently answering the
question.